An Analysis of NBA Player Performance Using Principal Component Analysis

Introduction

• What is principal component analysis (PCA)?
• When and why was PCA first proposed?
• What dataset is being used?

Methods

• Data must be standardized
• Covariance matrix constructed
• Find eigenvalues and eigenvectors
• Create principal components

Methods: Standardization

• PCA creates linear combinations (t) of variables

\[t = c_{1}X_{1} + ... + c_{n}X_{n}; t = Xc\]

• X is the data set as a matrix
• c is a vector of different variables
• Maximum variance is the goal \[\underset{||c||=1}{argmax}(var(t)) \]

Methods: Covariance Matrix and Eigenvectors

• Covariance between two variables, X and Y, is calculated as follows: \[Cov(X,Y) = E[(X − E[X])(Y − E[Y])]\]
• A covariance matrix can be constructed

Data: Description

Data: Histograms

Data: Boxplots

Data: Correlation Matrix

Data: Best Performers

Data: Best Performers

Data: Best Performers

Analysis: Eigenvalues

Analysis: Variables

Analysis: What Makes Each PC

Analysis: What Makes Each PC

Analysis: What Makes Each PC

Analysis: What Makes Each PC

Analysis: Which Players Contribute Most

Analysis: Which Players Contribute Most

Analysis: Which Players Contribute Most

Analysis: Which Players Contribute Most

Analysis: Biplot

Challenges

• Standardization
• Loss of information
• Impact of outliers

Conclusion

• Utilizing PCA for a holistic view of player-performance relationships

• Harnessing diverse visualizations to illuminate player-metric connections

• Identifying correlations and eliminating redundancies among variables

• Understanding main axes (principal components) through eigenvectors

• Showcasing PCA as a powerful unsupervised learning method